When you divide complex numbers, like $a + bi$ by $c + di$, you often use something called the complex conjugate.

The complex conjugate of $c + di$ is $c - di$.

Why Should We Use Complex Conjugates?

1. Makes Things Simpler: When you multiply by the conjugate, it helps get rid of the imaginary part in the bottom part (denominator) of the fraction.

2. Results in a Real Denominator: After multiplying, you get a form like this: $\frac{(a + bi)(c - di)}{(c + di)(c - di)}$ Here, the bottom part becomes $c^2 + d^2$, which is a regular number (real number).

So, complex conjugates are really useful! They help turn tricky divisions into simpler, real numbers!